We consider the estimation of the transition matrix of a hidden Markovian process by using information geometry with respect to transition matrices. In this paper, only the histogram of $k$-memory data is used for the estimation. To establish our method, we focus on a partial observation model with the Markovian process and we propose an efficient estimator whose asymptotic estimation error is given as the inverse of projective Fisher information of transition matrices. This estimator is applied to the estimation of the transition matrix of the hidden Markovian process. In this application, we carefully discuss the equivalence problem for hidden Markovian process on the tangent space.
翻译:我们通过使用与过渡矩阵有关的信息几何方法来考虑对隐蔽的Markovian进程过渡矩阵的估算。 在本文中,只有用于估算的直方图 $k$-momory 数据。为了确定我们的方法,我们侧重于与Markovian进程有关的部分观察模型,我们建议一个高效的估算器,该估算器的天体估计误差被作为过渡矩阵的预测性渔业信息的反差。该估算器用于估算隐蔽的Markovian进程的过渡矩阵。在这个应用中,我们仔细讨论了隐蔽的Markovian进程在相近空间的等值问题。